A new cultivar of nectarine tree called ‘Amoore Sweet’ is described herein. The new cultivar originated from a hand-pollinated cross of Ark. 699N (non-patented, unreleased genotype) (female parent)×Ark. 663CN (non-patented, unreleased genotype) (male parent) made in 2001. The seeds resulting from this controlled hybridization were germinated in a greenhouse in the late winter 2001/early spring of 2002 and planted in a field near Clarksville, Ark. The seedlings fruited during the summer of 2004 and one seedling, designated Ark. 765, was selected for its very firm, non-melting yellow flesh, early-mid season ripening, medium-sized fruits, excellent fruit quality with distinct low-acid nectarine flavor, and resistance to bacterial spot disease.